In Exercise 8.109, the average hourly wage for public school cafeteria workers was given as $10.33.26 If n  40 randomly selected public school cafeteria workers within one school district are found to have an average hourly wage of x̅ = $9.75 with a standard deviation of s = $1.65, would this information contradict the reported average of $10.33?

a. What are the null and alternative hypotheses to be tested?

b. Use the Large-Sample Test of a Population Mean applet to find the observed value of the test statistic.

c. Use the Large-Sample Test of a Population Mean applet to find the p-value of this test.

d. Based on your results from part c, what conclusions can you draw about the average hourly wage of $10.33?